Publicación: VELOCITY-VORTICITY-PRESSURE FORMULATION FOR THE OSEEN PROBLEM WITH VARIABLE VISCOSITY
Fecha
2021
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Editor
CALCOLO
Resumen
WE PROPOSE AND ANALYSE AN AUGMENTED MIXED FINITE ELEMENT METHOD FOR THE OSEEN EQUATIONS WRITTEN IN TERMS OF VELOCITY, VORTICITY, AND PRESSURE WITH NON-CONSTANT VISCOSITY AND HOMOGENEOUS DIRICHLET BOUNDARY CONDITION FOR THE VELOCITY. THE WEAK FORMULATION INCLUDES LEAST-SQUARES TERMS ARISING FROM THE CONSTITUTIVE EQUATION AND FROM THE INCOMPRESSIBILITY CONDITION, AND WE SHOW THAT IT SATISFIES THE HYPOTHESES OF THE BABU?KA-BREZZI THEORY. REPEATING THE ARGUMENTS OF THE CONTINUOUS ANALYSIS, THE STABILITY AND SOLVABILITY OF THE DISCRETE PROBLEM ARE ESTABLISHED. THE METHOD IS SUITED FOR ANY STOKES INF-SUP STABLE FINITE ELEMENT PAIR FOR VELOCITY AND PRESSURE, WHILE FOR VORTICITY ANY GENERIC DISCRETE SPACE (OF ARBITRARY ORDER) CAN BE USED. A PRIORI AND A POSTERIORI ERROR ESTIMATES ARE DERIVED USING TWO SPECIFIC FAMILIES OF DISCRETE SUBSPACES. FINALLY, WE PROVIDE A SET OF NUMERICAL TESTS ILLUSTRATING THE BEHAVIOUR OF THE SCHEME, VERIFYING THE THEORETICAL CONVERGENCE RATES, AND SHOWING THE PERFORMANCE OF THE ADAPTIVE ALGORITHM GUIDED BY RESIDUAL A POSTERIORI ERROR ESTIMATION.
